Preface
Chapter 1. Once Over Lightly
1-1. Diophantine Equations and the Genus of an Algebraic Plane Curve
1-2. Zeros and Critical Points of Analytic Functions of One Complex Variable
1-3. Some General Problems of Nonlinear Analysis
1-4. Applications of Nonlinear Problems
Chapter 2. Finite Dimensional Systems in H
2-1. The Definition of Degree of a Mapping
2-2. Some Properties of the Degree of a Mapping
2-3. Gradient Systems and Their Basic Properties
2-^. Gradient Systems with Nondegenerate Critical Points
2-5. Critical Points for General Gradient Systems
2-6. Systems Deformable to Gradient Systems
Chapter 3. Infinite Dimensional Systems
3-1. The Degree of a Class of Operators in Spaces of Infinite Dimension
3-2. A Special Class of Noncompact Operators
3-3 Gradient Operators and Their Properties
3-4. A Remark on the Theory of Critical Points of Infinite Dimensional Gradient Operators
3-5. Local Behavior of Nonlinear Operator Equations in Hilbert Space
Chapter 4 Applications
4-1. Global Univalence
4-2. Topics in Nonlinear Autonomous Ordinary Differential Equations
4-3. Topics in Elliptic Partial Differential Equations
Appendix I. The Axioms of Homology Theory
Appendix II. Standard Results from Analysis